Waiting times in a branching process model of colorectal cancer initiation

We study a multi-type branching process model for the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting time distributions of novel driver mutations. The approach presented here is relevant to the study of finite-time properties of multi-type branching process models in which growth rates of consecutive types are non-decreasing.